The instrument is a Geiger counter and is used to measure radioactive level around people's bodies.
(a) Let
be the maximum linear speed with which the ball can move in a circle without breaking the cord. Its centripetal/radial acceleration has magnitude

where
is the radius of the circle.
The tension in the cord is what makes the ball move in its plane. By Newton's second law, the maximum net force on it is

so that

Solve for
:

(b) The net force equation in part (a) leads us to the relation

so that
is directly proportional to the square root of
. As the radius
increases, the maximum linear speed
will also increase, so the cord is less likely to break if we keep up the same speed.
<span>Active Galactic Nuclei.</span>
An object's momentum is the product of its mass and its velocity:
p = mv
p is its momentum, m is its mass, and v is its velocity.
Given values:
p = -80kg×m/s
m = 8kg
Plug in these values and solve for v:
-80 = 8v
v = -10m/s
Choice D